Research On Optimal Estimation Algorithm Of 2-D System With Complicated Multi-Channel Multiplicative Noise

Optimal estimation algorithm of two-dimensional (2-D) state space model with complicated multi-channel multiplicative noise was mainly studied in this dissertation. The system state of the two-dimensional (2-D) state space model is the function of two independent variables. Therefore, compared with 1-D model,2-D model is more complicated suitable for some practical systems. With the expansion of the scope of study objects for modern control theory, the research achievement based on 2-D state space model is becoming more and more abundant. The multiplicative noise is widely existed in the problems studied in 2-D model, for instance, the salt-and-pepper noise in the territory of image processing. Complicated multi-channel multiplicative noise can better describe the effect of the influence on the observations of system made by multi-channel multiplicative noise existing in multiple observation channel, hence this model is more suitable in the realities. Optimal estimation algorithm of 2-D system with complicated multi-channel multiplicative noise can solve the problem of optimal estimation in much more complex environment. The main work of the dissertation is as follows:1. Based on the 2-D FM-Ⅱ state space model with complicated multi-channel multiplicative noise, the state filtering algorithm of this model is deduced by using orthogonal projection theorem. The algorithm has recursive structure and can overcome the problem of "dimensional disaster" in previous method by adopting line by line state filtering sequence. The algorithm is convenient for realization on computer due to low computational complexity.2. Based on the 2-D FM-Ⅱ state space model with complicated multi-channel multiplicative noise, by using orthogonal projection theorem the observation noise filtering algorithm of the model is deduced. Based on the observation noise filtering algorithm, the fixed interval algorithm under single index changing of observation noise is derived by keeping on using projection theorem.3. The generalized 2-D Roesser state space model with complicated multi-channel multiplicative noise can be firstly transformed into two reduced order subsystems under equivalent transformation relation. One of the subsystems is FM-Ⅱ state space model with complicated multi-channel multiplicative noise, whose dynamic noise and observation noise could be correlated statistically at the same point on the two dimensional coordinate planes; The other subsystem is composed of the system noise of the original system. Based on the projection theorem the optimal state filtering algorithms of the two subsystems are derived. Consequently, the optimal state filtering algorithm of generalized 2-D Roesser state space model with complicated multi-channel multiplicative noise is derived by using the previous equivalent transformation relation.4. The above estimation algorithms are optimal in the sense of linear minimum variance. Simulation results verify the algorithms.